Bend extruded svg around sphere or extrude svg along sphere normals
I tried the suggested Solidify on a single-skin sphere, but I didn't manage to get the result I wanted. But I worked out a similar approach - with a little more work and without modifiers, that did the trick:

Create Sphere of approriate size
Use Boolean to cut off lower half to get to the desired half sphere and cut out the desired SVG symbol as I did before
Use &quot;Edit Mode&quot; to remove all inner vertices created by the booleans to produce a single skin sphere with cutout as suggested by Robin.

Duplicate the object, scale it so there is a second, slightly larger version of it - as desired for the thickness
Join the two objects and &quot;stitch&quot; the edges with CTRL-E - &quot;Bridge Edge loops&quot;

I had to select the inner cutouts manually, &quot;select loop&quot; didn't work there. But in the end, the result was worth the effort:

Thanks for your help, I hope somebody finds this useful!
UPDATE: I also found out why the solidify didn't work before, I didn't actually use a singleskin sphere (Step 3 from above), but instead I used a boolean operation to cut out the inner side with an only slightly smaller sphere. Which LOOKED single, but actually was a normal doubleskinned sphere. With the singleskinned sphere, it worked like a charm. So, thanks again Robin for the suggestion, you were spot on, if only I had done it right in the first place, this would have worked perfectly!
So, alternative to my more time-intensive method:

Create Sphere of approriate size
Use Boolean to cut off lower half to get to the desired half sphere and cut out the desired SVG symbol as I did before
Use &quot;Edit Mode&quot; to remove all inner vertices created by the booleans to produce a single skin sphere with cutout as suggested by Robin.
Switch back to &quot;Object Mode&quot; and use the Solidify modifier to get the desired effect with a lot less effort :).

Update 2: Yep, it works :)